PLz help me with this question?

Question

ok the question is....... g(x)= 2+ x + 4e^(x-2) , find g ^ - 1 (8)

so g^-1(8) =?

plz help me with this question

Answer 1

the answer is 2

g^-1(y) is basically asking what value of x will give you y
i.e. g(x)= 2+ x + 4e^(x-2)
g(x)=8
therefore, 8=2+x+4e^(x-2)
subtract 2
6=x+4e^(x-2)
good rule of thumb when you have a variable by itself and one up in an exponent or in a logarithm try to zero out the one in the log or exponent. here, we'll try 2 since x-2, 2-2=0
6=(2)+4e^((2)-2)
6=2+4e^0
6+2+4 (1)
6=6 Awesome x=2

Answer 2

g(8) = 2 + 8 + 4*e^(8-2) = 10 + 4e^6

g^-1(8) = 1 / g(8) = 1 over (10 + 4e^6)